If a specification doesn't have to depend on a specific (type of) device, then it probably shouldn't. Or it should be split in a dependent and an independent part. Device-independency is in many ways the same as accessibility, although for different reasons.
A specification like CSS is somewhat device-dependent: specifying a font only makes sense on a visual medium; there is no interpretation of font on a speech synthesizer. CSS in fact divides all devices into classes and allows styles for each class to be grouped. It is different for HTML. Precisely because CSS (and XSL) takes care of the device-dependent parts, HTML can be device-independent. Thanks to that, you can do a lot more with HTML than display it on a screen (see also repurposing).
It is sometimes claimed that HTML isn't device-independent, because an HTML author assumes that his reader has a convenient medium to read text, such as a book, a magazine, a laser printer or a reasonably large screen. Reading a 5-page article on the display of most mobile phones is not really pleasant. But is that HTML's fault, or is it just that certain content is more suitable for certain environments? HTML is just as capable of expressing weather reports as novels. What is blamed on HTML is probably just shortcomings in current style sheet implementations.
Not only is it desirable to be able to use a resource on different devices at the same time, but a valuable resource should also be designed to survive future changes in technology: with technology changing as fast as it does now, a document written on an up-to-date system 4 years ago may already be unreadable, because the hardware isn't made anymore, because the software maker has gone broke, etc. Not all HTML files are worth keeping for 50 years, but HTML should at least make it possible that documents written in it are still readable for the next generation(s). Gutenberg's bible is still readable after 500 years, why should your publications be worth any less? (See also longevity.)